This article describes the design of a linear observer‐linear controller‐based robust output feedback scheme for output reference trajectory tracking tasks in an omnidirectional mobile robot. The unknown, possibly state‐dependent, additive nonlinearities influencing the input‐output tracking error dynamics are modeled as an absolutely bounded, additive, unknown “time‐varying disturbance” input signal. This procedure simplifies the system tracking error description to that of three independent chains of second order integrators with, known, position‐dependent control gains. These simplified systems are additively perturbed by the unknown, smooth, time‐varying signal which is proven to be trivially observable. Generalized proportional integral (GPI) observers, are shown to naturally estimate, in an arbitrarily close manner, the unknown perturbation input of the simplified system and a certain number of its time derivatives. This information is used to advantage on the linear, observer‐based, feedback controller design via a simple cancellation effort. The results are implemented on a laboratory prototype of an omnidirectional mobile robot.

This article describes the design of a linear observer-linear controller-based robust output feedback scheme for output reference trajectory tracking tasks in an omnidirectional mobile robot. The unknown, possibly state-dependent, additive nonlinearity influencing the input-output tracking error dynamics, is modeled as an absolutely bounded, additive, unknown "time-varying disturbance" input signal. This procedure simplifies the system tracking error description to that of three independent chains of second order integrators with, known, position-dependent control gains, while additively being perturbed by the unknown, smooth, time-varying signal which is proven to be trivially observable. The total state-dependent uncertain input is assumed to be locally approximated by an arbitrary element of, a, fixed, sufficiently high degree family of Taylor polynomials for which a linear observer with a corresponding self-updating internal model may be readily designed. Generalized Proportional Integral (GPI) observers, which are the dual counterpart of GPI controllers (see [1]), are shown to naturally estimate, in a arbitrarily close manner, the unknown perturbation input of the simplified system and a certain number of its time derivatives, thanks to its embedded, internal time-polynomial model of the unknown, state-dependent, perturbation input. This information is used to advantage on the linear, observer-based, feedback controller design via a simple cancelation effort. The results are implemented on a laboratory prototype in a trajectory tracking problem.

This article describes the design of a linear observerlinear controller-based robust output feedback scheme for output reference trajectory tracking tasks in an input delayed omnidirectional mobile robot. The unknown, possibly state-dependent, additive nonlinearity influencing the tracking error dynamics, is modeled as an absolutely uniformly bounded, additive unknown "time-varying disturbance" input signal. This procedure simplifies the system tracking error description to that of three independent chains of second order integrators with, known, position-dependent control input gain matrix, while additively being perturbed by the unknown, smooth, time-varying signal. A GPI observer is the basis of a suitable perturbation prediction scheme, aimed at perturbation cancelation in the forward system, which allows to reduce the nonlinear delayed input control problem to that of a weakly perturbed linear delayed system. The approximate cancelation of the perturbation input facilitates the use of the classical Smith Predictor Compensator in the resulting dominantly linear problem. The results are implemented on a laboratory prototype.